Improved phase shift approach to the energy correction of the infinite order sudden approximation

Journal Article · Tue Jul 15 04:00:00 EDT 1980 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.440189· OSTI ID:5328176

Chang, B; Eno, L; Rabitz, H

A new method is presented for obtaining energy corrections to the infinite order sudden (IOS) approximation by incorporating the effect of the internal molecular Hamiltonian into the IOS wave function. This is done by utilizing the JWKB approximation to transform the Schroedinger equation into a differential equation for the phase. It is found that the internal Hamiltonian generates an effective potential from which a new improved phase shift is obtained. This phase shift is then used in place of the IOS phase shift to generate new transition probabilities. As an illustration the resulting improved phase shift (IPS) method is applied to the Secrest--Johnson model for the collinear collision of an atom and diatom. In the vicinity of the sudden limit, the IPS method gives results for transition probabilities, P/sub n/..-->..n+..delta..n, in significantly better agreement with the 'exact' close coupling calculations than the IOS method, particularly for large ..delta..n. However, when the IOS results are not even qualitatively correct, the IPS method is unable to satisfactorily provide improvements.

• Research Organization: Chemistry Department, Princeton University, Princeton, New Jersey 08544
• OSTI ID: 5328176
• Journal Information: J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 73:2; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

640304* -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
ATOM COLLISIONS
ATOM-MOLECULE COLLISIONS
COLLISIONS
DIFFERENTIAL EQUATIONS
ENERGY-LEVEL TRANSITIONS
EQUATIONS
MECHANICS
MOLECULE COLLISIONS
PHASE SHIFT
QUANTUM MECHANICS
SUDDEN APPROXIMATION